CN110261083B - Vision-based method for measuring vibration force suppression effect of magnetic suspension rotor - Google Patents
Vision-based method for measuring vibration force suppression effect of magnetic suspension rotor Download PDFInfo
- Publication number
- CN110261083B CN110261083B CN201910511660.9A CN201910511660A CN110261083B CN 110261083 B CN110261083 B CN 110261083B CN 201910511660 A CN201910511660 A CN 201910511660A CN 110261083 B CN110261083 B CN 110261083B
- Authority
- CN
- China
- Prior art keywords
- rotor
- displacement
- same
- local
- directions
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 239000000725 suspension Substances 0.000 title claims abstract description 32
- 230000001629 suppression Effects 0.000 title claims abstract description 14
- 238000000034 method Methods 0.000 title claims abstract description 13
- 238000006073 displacement reaction Methods 0.000 claims abstract description 41
- 230000010363 phase shift Effects 0.000 claims description 19
- 238000012546 transfer Methods 0.000 claims description 17
- 230000035945 sensitivity Effects 0.000 claims description 12
- 238000005339 levitation Methods 0.000 claims description 10
- 238000000691 measurement method Methods 0.000 claims description 5
- 230000004069 differentiation Effects 0.000 claims description 3
- 238000000605 extraction Methods 0.000 claims description 3
- 238000001914 filtration Methods 0.000 claims description 3
- 238000012545 processing Methods 0.000 claims description 2
- 229910000831 Steel Inorganic materials 0.000 claims 1
- 239000010959 steel Substances 0.000 claims 1
- 238000005259 measurement Methods 0.000 abstract description 17
- 238000005516 engineering process Methods 0.000 abstract description 9
- 230000000694 effects Effects 0.000 abstract description 3
- 230000006870 function Effects 0.000 description 25
- 238000010586 diagram Methods 0.000 description 4
- 230000000007 visual effect Effects 0.000 description 4
- 238000012986 modification Methods 0.000 description 2
- 230000004048 modification Effects 0.000 description 2
- 230000006978 adaptation Effects 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 230000001419 dependent effect Effects 0.000 description 1
- 230000008030 elimination Effects 0.000 description 1
- 238000003379 elimination reaction Methods 0.000 description 1
- 238000012827 research and development Methods 0.000 description 1
- 238000013519 translation Methods 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G01—MEASURING; TESTING
- G01M—TESTING STATIC OR DYNAMIC BALANCE OF MACHINES OR STRUCTURES; TESTING OF STRUCTURES OR APPARATUS, NOT OTHERWISE PROVIDED FOR
- G01M13/00—Testing of machine parts
Landscapes
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Magnetic Bearings And Hydrostatic Bearings (AREA)
Abstract
The invention discloses a method for measuring the suppression effect of vibration force of a magnetic suspension rotor based on vision, which is used for dynamically modeling a system containing the magnetic suspension rotor with unbalanced mass, taking the same-frequency bearing force as a direct control target, achieving the purpose of effectively eliminating the same-frequency vibration force and providing that the vibration is measured by adopting a vision vibration measurement technology. The invention can be used for a rotor system taking a magnetic bearing as a supporting structure, not only considers the current rigidity force, but also considers the residual rigidity force caused by displacement, can more effectively inhibit the same-frequency vibration force, realizes non-contact measurement by adopting a vibration measurement technology based on vision, and verifies the effect of a same-frequency vibration control algorithm.
Description
Technical Field
The invention relates to a visual measurement method for zero-force control of same-frequency vibration of a magnetic suspension rotor system, and belongs to the field of magnetic suspension control technology and measurement.
Background
Vibration in a magnetic levitation rotor system is a problem of great concern, and common-frequency vibration is mainly caused by mass unbalance of a magnetic levitation rotor. When the rotor rotates, vibration force can be transmitted to the mechanical shell, the precision and the performance of the magnetic bearing device are affected, and even the magnetic bearing device collides with a machine shell to cause some dangerous accidents. Aiming at the control of the vibration of the magnetic suspension rotor, many researchers provide different methods, such as Least Mean Square (LMS) algorithm, repeated learning algorithm, and the addition of compensation of same-frequency displacement stiffness force in a current loop to eliminate same-frequency vibration force. The minimum mean square algorithm realizes the elimination of the stiffness force of the same-frequency current by generating the same-frequency signals with equal gain and opposite phase and feedforward compensating the same-frequency current, but the method does not consider the vibration generated by the displacement stiffness force and cannot give consideration to the requirements of system stability and convergence speed; the repeated learning algorithm adjusts the gain through self-adaptive learning, and although the suppression of the same-frequency current can be realized, the residual rigidity force caused by displacement cannot be eliminated; some trap-based same-frequency vibration control also only considers compensating current stiffness. Therefore, in order to better suppress the same-frequency vibration force in the magnetic suspension rotor system, not only the current stiffness but also the displacement stiffness need to be compensated.
The vibration measurement is usually carried out by adopting an accelerometer to carry out contact measurement, the measurement precision is relatively high, but when the mass of a measured object is small, the measurement result is influenced due to the addition of the mass of the accelerometer; when measuring large objects, surface mounting a large number of accelerometers can be time consuming and labor intensive. And in some dangerous occasions such as high temperature, high pressure, vacuum, etc., it is not suitable to adopt the accelerometer to measure. The vibration measurement technology based on vision is widely applied with the advantages of low cost, good flexibility, remote measurement and the like, and compared with an accelerometer, the vision measurement technology can not cause mass load effect, can greatly save labor force, and is suitable for dangerous occasions such as high temperature and high pressure. By adopting the zero-force control and visual measurement method for the same-frequency vibration of the magnetic suspension rotor system of the wave trap, not only the current stiffness force is considered, but also the residual stiffness force generated by displacement is considered, so that the same-frequency vibration force can be effectively controlled, and the vibration suppression effect can be verified. The visual measurement technology is applied to the technical field of magnetic suspension control, and has extremely important significance for future research and development.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the invention provides a method for measuring the suppression effect of the vibration force of a magnetic suspension rotor based on vision.
The technical scheme is as follows: in order to achieve the purpose, the invention adopts the technical scheme that:
a magnetic suspension rotor vibration force suppression effect measurement method based on vision comprises the following steps:
step 1, establishing a magnetic suspension rotor dynamic model containing same-frequency vibration force according to rotor mass, rotor displacement, displacement rigidity, current rigidity and displacement deviation generated by disturbance by taking same-frequency bearing force as a bridge;
step 2, using the same-frequency bearing force as a direct control target, inputting the constructed same-frequency bearing force F(s) into a wave trap to inhibit the same-frequency vibration, wherein the closed-loop transfer function of the system is as follows:
wherein G(s) represents a closed loop transfer function of the magnetic suspension rotor control system in the X direction, s represents an independent variable in a complex domain, Gc(s) basic levitation controller, Gw(s) is the transfer function of the power amplifier, P(s) is the control object, N(s) is the transfer function of the wave trap, KiAX，KAXCurrent stiffness and displacement stiffness, respectively;
according to the closed-loop transfer function of the system, the characteristic equation of the system is obtained as follows:
D(s)＝1+Gc(s)Gw(s)KiAXP(s)-KAXGw(s)+KiAXN(s)Gw(s) (7)
wherein D(s) represents a characteristic equation of the magnetic suspension rotor control system in the X direction.
And 3, based on the closed-loop transfer function of the system obtained in the step 2, with same-frequency disturbance d(s) as input and bearing force F(s) as output, the sensitivity function of the system is as follows:
wherein S(s) represents a sensitivity function of the system;
taking equation (8) into equation (7), the system stability condition with respect to the trap phase shift angle is obtained:
wherein arc [ s(s) ] is the phase angle of the sensitivity function, β is the phase shift angle of the trap; according to the formula (15), the system stability can be realized only by adjusting the phase shift angle of the wave trap;
step 4, taking a video image sequence controlled by the vibration of the magnetic suspension rotor system as input, and filtering by adopting a Gabor filter to obtain a local amplitude and a local phase of local motion; at t0At the moment, the image intensity values of the image sequence in the video are I (x, y, t)0) Performing convolution processing on the two-dimensional Gabor filter and the image intensity to obtain an image at the time t0The frequency domain form with the direction θ:
wherein A is0(x,y,t0) Is the local amplitude, phi (x, y, t)0) Is a local phase, Gθ+iHθIn complex form with a Gabor filter, i denotes the imaginary unit, and the Gabor filter is expressed as:
g(x,y；λ,θ,ψ,σ,γ)＝Gθ+iHθ (17)
wherein x, y represent spatial position, λ represents wavelength of sine wave, θ represents direction of parallel stripes in Gabor filter kernel, ψ represents phase shift, σ represents standard deviation of gaussian function, and γ represents spatial aspect ratio;
Gθ,Hθcomprises the following steps:
the function of the Gabor filter is specifically expressed as
Wherein x and y represent spatial positions, theta represents the direction of parallel stripes in a Gabor filter kernel, lambda represents the wavelength of a sine wave, psi represents phase shift, and gamma represents a spatial aspect ratio; σ denotes the standard deviation of the Gaussian function, xθ,yθIs a space vector, expressed as:
and 5, performing motion extraction according to the obtained local phase, and extracting the displacement of the local motion in the horizontal direction and the vertical direction, wherein the speed of the local motion in the horizontal direction and the vertical direction is as follows:
wherein u and v are the velocities in the horizontal and vertical directions, respectively,
to a local phase
The differentiation in the horizontal direction with respect to x and the time t,
to a local phase
Differentiation of y and t in the vertical direction;
the displacements of the local motion in the horizontal and vertical directions are extracted by integrating the velocities in the horizontal and vertical directions.
Preferably: the method for establishing the magnetic suspension rotor dynamic model containing the same-frequency vibration force in the step 1 comprises the following steps:
step 11, the central surface of the rotor is pi, and the central surfaces of the first radial magnetic bearing electromagnet A and the second radial magnetic bearing electromagnet B are pi respectively1、Π2The stator middle connecting line of A and B is crossed with N, the rotor geometric axis is crossed with N and N1，Π2Respectively cross over C and C1,C2Establishing an inertial coordinate system NXY by taking a geometric center N of the stator as an origin, a vertical direction as a Y axis and a horizontal direction as an X axis, and establishing a rotating coordinate system O epsilon eta rotating at a rotor rotating speed omega by taking a geometric center O of the rotor as an origin, wherein epsilon represents a horizontal coordinate of the rotating coordinate system, and an included angle between epsilon and the horizontal direction is omega t; η represents the ordinate of the rotating coordinate system, perpendicular to the abscissa e.
Step 12, obtaining a dynamic model of the rotor in the radial directions X and Y according to Newton's second law:
where m is the mass of the rotor, x is the displacement of the center of mass of the rotor, FAX,FAYBearing forces in the X, Y directions of the rotor are expressed as:
wherein, KAX,KAYRespectively, the displacement stiffness in the X, Y directions, KiAX,KiAYCurrent stiffness in the X, Y directions, respectively, thetaAX,ΘAYRespectively displacement deviation generated by same-frequency disturbance in X and Y directions and same-frequency disturbance amount theta on X and Y channelsAX(t)，ΘAY(t) are respectively:
wherein l is the distance from the geometric center O to the mass center C, t represents the time, theta represents the phase shift angle generated by mass unbalance, and omega represents the rotor rotation speed;
step 13, bringing the formula (2) into the formula (1) to obtain a magnetic suspension rotor dynamic model of the rotor containing the same-frequency vibration force:
wherein m is the mass of the rotor,
second derivatives of the displacement in the X, Y directions, XAX,xAYRespectively, displacement in X and Y directions, KAX,KAYThe displacement stiffness in the X and Y directions, kiAX,KiAYCurrent stiffness in X, Y directions, respectively, thetaAX,ΘAYThe displacement deviation i caused by the disturbance in X and Y directionsAX，iAYThe current magnitudes in the X and Y directions are respectively. Preferably: in step 2, the transfer function of the notch filter N(s) is:
where ρ is the trap gain coefficient, s represents the argument in the complex domain, β is the phase shift angle of the trap, and Ω is the rotor rotation speed.
Preferably: method for acquiring the speed of the local movement in the horizontal direction and the vertical direction in step 5:
at time t, the image intensity value with local position (x, u) is I (x, y, t), the local phase with respect to the displacement signal is a constant, and the local phase obtained according to equation (16) can be obtained:
φθ(x,y,t)＝C (21)
where C is a constant, and x, y, and t are differentiated on both sides of equation (21), respectively, so as to obtain:
wherein u, v are the velocities in the horizontal direction and the vertical direction, respectively, when the following conditions are satisfied:
the velocities u, v of the local movement in the horizontal direction and in the vertical direction are determined.
Compared with the prior art, the invention has the following beneficial effects:
1) the same-frequency vibration force generated by the unbalanced mass of the magnetic suspension rotor can be effectively eliminated, the bearing force constructed is directly input into the wave trap, the phase shift angle is introduced to effectively compensate the defined system sensitivity function phase, and the problem that the wave trap influences the stability of the system can be solved.
2) The vibration measurement technology based on vision can realize non-contact measurement, greatly reduces labor cost, and is suitable for dangerous occasions such as high temperature, high pressure and the like.
Drawings
FIG. 1 is a schematic diagram of a magnetic levitation rotor structure in a magnetic levitation model according to the present invention;
FIG. 2 is a schematic diagram of an inertial coordinate system established based on a magnetic suspension model according to the present invention;
fig. 3 is a schematic diagram of vibration control based on a wave trap in the present invention.
Detailed Description
The present invention is further illustrated by the following description in conjunction with the accompanying drawings and the specific embodiments, it is to be understood that these examples are given solely for the purpose of illustration and are not intended as a definition of the limits of the invention, since various equivalent modifications will occur to those skilled in the art upon reading the present invention and fall within the limits of the appended claims.
A magnetic suspension rotor vibration force suppression effect measurement method based on vision mainly analyzes rotor dynamics in a radial translation direction and influence of same-frequency vibration because rotor mass imbalance and influence of other factors are most serious in the radial direction, and comprises the following steps:
step one, establishing a dynamic model of a magnetic suspension rotor containing same-frequency vibration
The magnetic suspension rotor structure is shown in figure 1: the central surfaces of the rotor and the radial magnetic bearing electromagnets A and B are pi respectively1，Π2. Stator middle connecting lines pi and cross N of A and B, and rotor geometric axes pi and pi1，Π2Respectively cross over C and C1,C2Establishing an inertial coordinate system NXY by taking a geometric center N of a stator as an original point, establishing a rotating coordinate system O epsilon eta rotating by a rotor rotating speed omega by taking a geometric center O of a rotor as an original point, wherein epsilon represents a horizontal coordinate of the rotating coordinate system, and an included angle between epsilon and the horizontal direction is omega t; η represents the ordinate of the rotating coordinate system, perpendicular to the abscissa e, as shown in fig. 2.
According to newton's second law, a dynamic model of the rotor in the radial directions X, Y can be obtained:
where m is the mass of the rotor and x is the displacement of the center of mass of the rotor. FAX,FAYThe bearing forces in the X, Y directions of the rotor, respectively, can be expressed as:
wherein, KAX,KAYRespectively, the displacement stiffness in the X, Y directions, KiAX,KiAYCurrent stiffness in the X, Y directions, respectively. Wherein, thetaAX,ΘAYDisplacement deviation generated by same-frequency disturbance in X and Y directions respectively, and same-frequency disturbance quantity on X and Y channels respectively are as follows:
Taking equation (2) into equation (1), the dynamic model of the rotor in the radial directions X and Y can be specifically expressed as:
and step two, based on the step one, with the bearing force as a direct control target, designing a vibration control algorithm based on the wave trap to inhibit the same-frequency vibration.
The vibration suppression block diagram based on the wave trap, using a single channel as an example, is shown in fig. 3, Gc(s) basic levitation controller, which mainly controls the rotor to stably levitate, Gw(s) is a transfer function of the power amplifier, P(s) is a control object, rho is a gain coefficient of the wave trap, and theta(s) is a same-frequency disturbance signal. The same frequency bearing force is taken as a direct control target, the constructed same frequency bearing force F(s) is input to a wave trap, and the same frequency K is obtained by the formula (2)xΘAX+KiiAXΘAXThe effective suppression is obtained after the wave trap N(s). The transfer function of the trap n(s) is:
where s represents the independent variable in the complex domain and β is the phase shift angle of the trap, which can be used to compensate the phase of the system sensitivity function at different rotational speeds.
The closed loop transfer function of the system is:
the characteristic equation of the system obtained from equation (6) is:
D(s)＝1+Gc(s)Gw(s)KiAXP(s)-KAXGw(s)+KiAXN(s)Gw(s) (7)
step three, based on the step two, combining a system sensitivity function to give a stable condition of the system;
with the same-frequency disturbance theta(s) as input and the bearing force F(s) as output, defining the sensitivity function of the system as follows:
where s(s) represents the system sensitivity function, equation (7) brings into equation (8), which can be obtained:
D(s)＝ρS(s)(scosβ+Ωsinβ)+s2+Ω2＝0 (9)
when the trap gain ρ → 0, s ═ j Ω can be obtained, (j represents an imaginary unit, j represents an imaginary unit21) regarding the trap gain p as an independent variable and s as a dependent variable, when p tends to 0, differentiating p can obtain the variation trend of s along with the trap gain p around s ═ j Ω:
wherein,
from equation (10), the phase angle can be found:
where arc [ S(s) ] is the phase angle of the sensitivity function.
When the closed-loop characteristic root is located on the left half plane of the s plane, the system is stable, namely:
by substituting equation (13) for equation (14), the system stability condition with respect to the trap phase shift angle can be obtained:
Step four, acquiring a video image sequence based on the magnetic suspension rotor vibration control of the wave trap, and taking the video image sequence as input, filtering by adopting a Gabor filter, and solving the amplitude and the phase of local motion;
the local phase corresponds to the local motion, which can be calculated from the local phase, from which the local phase of the spatial motion can be extracted by a Gabor filter. Let us assume at t0At the moment, the image intensity values of the video image sequence are I (x, y, t)0) Convolving the two-dimensional Gabor filter and the image intensity to obtain each frame of image at time t0The frequency domain form with the direction θ:
wherein A is0(x,y,t0) Is the spatial local amplitude, phi (x, y, t)0) For the spatial local phase, motion information in different directions can be extracted through a Gabor filter. Gθ+iHθIs the complex form of a Gabor filter, i denotes the imaginary unit, which can be expressed as:
g(x,y；λ,θ,ψ,σ,γ)＝Gθ+iHθ (17)
wherein G isθ,HθComprises the following steps:
the function of the two-dimensional Gabor filter can be expressed specifically as
Where x, y denote spatial position, θ denotes the direction of the parallel fringes in the Gabor filter kernel, λ denotes the wavelength of the sine wave, and ψ denotes phase shift. γ represents the spatial aspect ratio, mainly determining the shape of the Gabor function; σ represents the standard deviation of the gaussian function and mainly determines the size of the acceptable region of the Gabor filter kernel. x is the number ofθ,yθIs a space vector, which can be expressed as:
and fifthly, motion extraction is carried out through the obtained local phase, and displacements of the local motion in the horizontal direction and the vertical direction are extracted.
At an arbitrary time t, the image intensity value with the spatial local position (x, y) is I (x, y, t), the local phase with respect to the displacement signal is a constant, and the local phase obtained according to equation (16) can be obtained:
φθ(x, y, t) ═ C (21) where,
c is a constant, and x, y, and t are differentiated on both sides of equation (21), respectively, to obtain:
wherein u, v are the velocities in the horizontal direction and the vertical direction, respectively, when the following conditions are satisfied:
and solving the speed of the local motion in the horizontal direction and the vertical direction as follows:
wherein,
representing local phase
The differentiation of x and t in the horizontal direction,
representing local phase
Differentiation of y and t in the vertical direction.
The displacements of the local motion in the horizontal and vertical directions can be extracted by integrating the velocities in the horizontal and vertical directions.
The invention carries out dynamic modeling on a system containing the magnetic suspension rotor with unbalanced mass, takes the same-frequency bearing force as a direct control target, realizes the aim of effectively eliminating the same-frequency vibration force, and provides the adoption of a visual vibration measurement technology to measure the vibration. The invention can be used for a rotor system taking a magnetic bearing as a supporting structure, not only considers the current rigidity force, but also considers the residual rigidity force caused by displacement, can more effectively inhibit the same-frequency vibration force, realizes non-contact measurement by adopting a vibration measurement technology based on vision, and verifies the effect of a same-frequency vibration control algorithm.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.
Claims (4)
1. A magnetic suspension rotor vibration force suppression effect measurement method based on vision is characterized by comprising the following steps:
step 1, establishing a magnetic suspension rotor dynamic model containing same-frequency vibration force according to rotor mass, rotor displacement, displacement rigidity, current rigidity and displacement deviation generated by disturbance by taking same-frequency bearing force as a bridge;
step 2, using the same-frequency bearing force as a direct control target, inputting the constructed same-frequency bearing force F(s) into a wave trap to inhibit the same-frequency vibration, wherein the closed-loop transfer function of the system is as follows:
wherein G(s) represents a closed loop transfer function of the magnetic suspension rotor control system in the X direction, s represents an independent variable in a complex domain, Gc(s) basic levitation controller, Gw(s) is the transfer function of the power amplifier, P(s) is the control object, N(s) is the transfer function of the wave trap, KiAXFor current stiffness, KAXIs the displacement stiffness;
according to the closed-loop transfer function of the system, the characteristic equation of the system is obtained as follows:
D(s)＝1+Gc(s)Gw(s)KiAXP(s)-KAXGw(s)+KiAXN(s)Gw(s) (7)
wherein D(s) represents a characteristic equation of the magnetic suspension rotor control system in the X direction;
and 3, based on the closed-loop transfer function of the system obtained in the step 2, taking the same-frequency disturbance d(s) as input and the same-frequency bearing force F(s) as output, wherein the sensitivity function of the system is as follows:
wherein S(s) represents a sensitivity function of the system;
taking equation (8) into equation (7), the system stability condition with respect to the trap phase shift angle is obtained:
wherein arc [ s(s) ] is the phase angle of the sensitivity function, β is the phase shift angle of the trap; according to the formula (15), the system stability can be realized only by adjusting the phase shift angle of the wave trap;
step 4, taking a video image sequence controlled by the vibration of the magnetic suspension rotor system as input, and filtering by adopting a Gabor filter to obtain a local amplitude and a local phase of local motion; at t0At the moment, the image intensity values of the image sequence in the video are I (x, y, t)0) Performing convolution processing on the two-dimensional Gabor filter and the image intensity to obtain an image at the time t0The frequency domain form with the direction θ:
wherein A is0(x，y，t0) Is the local amplitude, phi (x, y, t)0) Is a local phase, Gθ+iHθIn complex form with a Gabor filter, i denotes the imaginary unit, and the Gabor filter is expressed as:
g(x，y；λ，θ，ψ，σ，γ)＝Gθ+iHθ (17)
wherein x, y represent spatial position, λ represents wavelength of sine wave, θ represents direction of parallel stripes in Gabor filter kernel, ψ represents phase shift, σ represents standard deviation of gaussian function, and γ represents spatial aspect ratio;
Gθ，Hθcomprises the following steps:
the function of the Gabor filter is specifically expressed as
Wherein x and y represent spatial positions, theta represents the direction of parallel stripes in a Gabor filter kernel, lambda represents the wavelength of a sine wave, psi represents phase shift, and gamma represents a spatial aspect ratio; σ denotes the standard deviation of the Gaussian function, xθ，yθIs a space vector, expressed as:
and 5, performing motion extraction according to the obtained local phase, and extracting the displacement of the local motion in the horizontal direction and the vertical direction, wherein the speed of the local motion in the horizontal direction and the vertical direction is as follows:
wherein u and v are the velocities in the horizontal and vertical directions, respectively,
to a local phase
The differentiation in the horizontal direction with respect to x and the time t,
to a local phase
Differentiation of y and t in the vertical direction;
the displacements of the local motion in the horizontal and vertical directions are extracted by integrating the velocities in the horizontal and vertical directions.
2. The vision-based method for measuring the vibration force suppression effect of the magnetic levitation rotor as recited in claim 1, wherein: the method for establishing the magnetic suspension rotor dynamic model containing the same-frequency vibration force in the step 1 comprises the following steps:
step 11, the central surface of the rotor is pi, and the central surfaces of a first radial magnetic bearing electromagnet A and a second radial magnetic bearing electromagnet B are pi respectively1、Π2The middle connecting line of the stators of the radial magnetic bearing electromagnet I and the radial magnetic bearing electromagnet II is intersected with the geometric center N of the stators, the geometric axis of the rotor is also intersected with pi, pi1，Π2Respectively cross over C and C1，C2Establishing an inertial coordinate system NXY by taking a geometric center N of the stator as an origin, a vertical direction as a Y axis and a horizontal direction as an X axis, and establishing a rotating coordinate system O epsilon eta rotating at a rotor rotating speed omega by taking a geometric center O of the rotor as an origin, wherein epsilon represents a horizontal coordinate of the rotating coordinate system, and an included angle between epsilon and the horizontal direction is omega t; eta represents the ordinate of the rotating coordinate system, which is perpendicular to the abscissa epsilon;
step 12, obtaining a dynamic model of the rotor in the radial directions X and Y according to Newton's second law:
where m is the mass of the rotor, x is the displacement of the center of mass of the rotor, FAX，FAYBearing forces in the X, Y directions of the rotor are expressed as:
wherein, KAX，KAYAre respectively displacement steel in X and Y directionsDegree, KiAX，KiAYCurrent stiffness in the X, Y directions, respectively, thetaAX，ΘAYRespectively displacement deviation generated by same-frequency disturbance in X and Y directions and same-frequency disturbance amount theta on X and Y channelsAX(t)，ΘAY(t) are respectively:
where l is the distance from the geometric center O to the center of mass C, t represents the time, θ1Represents the phase offset angle resulting from mass imbalance, Ω is the rotor rotational speed;
step 13, bringing the formula (2) into the formula (1) to obtain a magnetic suspension rotor dynamic model of the rotor containing the same-frequency vibration force:
wherein m is the mass of the rotor,
second derivatives of the displacement in the X, Y directions, XAX，xAYRespectively, displacement in X and Y directions, KAX，KAYRespectively, the displacement stiffness in the X and Y directions, KiAX，KiAYCurrent stiffness in X, Y directions, respectively, thetaAX，ΘAYThe displacement deviation i caused by the disturbance in X and Y directionsAX，iAYThe current magnitudes in the X and Y directions are respectively.
3. The vision-based method for measuring the vibration force suppression effect of the magnetic levitation rotor as recited in claim 2, wherein: the trap transfer function in step 2 is:
where ρ is the trap gain coefficient, s represents the argument in the complex domain, β is the phase shift angle of the trap, and Ω is the rotor rotation speed.
4. The vision-based method for measuring the vibration force suppression effect of the magnetic levitation rotor as recited in claim 3, wherein: method for acquiring the speed of the local movement in the horizontal direction and the vertical direction in step 5:
at time t, the image intensity value with local position (x, y) is I (x, y, t), the local phase with respect to the displacement signal is a constant, and the local phase obtained according to equation (16) can be obtained:
φθ(x，y，t)＝C (21)
where C is a constant, and x, y, and t are differentiated on both sides of equation (21), respectively, so as to obtain:
wherein u, v are the velocities in the horizontal direction and the vertical direction, respectively, when the following conditions are satisfied:
the velocities u, v of the local movement in the horizontal direction and in the vertical direction are determined.
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910511660.9A CN110261083B (en) | 2019-06-13 | 2019-06-13 | Vision-based method for measuring vibration force suppression effect of magnetic suspension rotor |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201910511660.9A CN110261083B (en) | 2019-06-13 | 2019-06-13 | Vision-based method for measuring vibration force suppression effect of magnetic suspension rotor |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN110261083A CN110261083A (en) | 2019-09-20 |
| CN110261083B true CN110261083B (en) | 2021-05-11 |
Family
ID=67918141
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201910511660.9A Active CN110261083B (en) | 2019-06-13 | 2019-06-13 | Vision-based method for measuring vibration force suppression effect of magnetic suspension rotor |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN110261083B (en) |
Families Citing this family (6)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN111060315A (en) * | 2019-11-28 | 2020-04-24 | 南京航空航天大学 | Mechanical fault diagnosis method based on vision |
| CN111353400B (en) * | 2020-02-24 | 2024-04-02 | 南京航空航天大学 | Full-scene vibration intensity spectrum analysis method based on visual vibration measurement |
| CN113124052B (en) * | 2021-04-16 | 2022-08-23 | 中国航空发动机研究院 | Method for controlling unbalance vibration of electromagnetic bearing-rotor system and electronic equipment |
| CN113188719B (en) * | 2021-04-21 | 2022-10-14 | 北京控制工程研究所 | Examine online dynamic balance system of accuse stator permanent-connection formula magnetic suspension rotary joint |
| CN113263921B (en) * | 2021-05-28 | 2022-07-15 | 同济大学 | Dynamic suspension control method of magnetic-levitation train combined with vibration identification |
| CN115978088B (en) * | 2023-03-20 | 2023-09-26 | 南昌航空大学 | Magnetic suspension rotor vibration control method based on self-adaptive bias and speed observer |
Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| SU435389A1 (en) * | 1972-05-22 | 1974-07-05 | Д. Ф. Сид ков | DEVICE FOR SUSPENSION ROTOR |
| CN1088308A (en) * | 1992-05-08 | 1994-06-22 | 蒂德裂纹试验装置公司 | Magnetic detection device for detecting cracks of ferromagnetic workpiece |
| US5400256A (en) * | 1992-01-21 | 1995-03-21 | The Charles Stark Draper Laboratory, Inc. | Frequency tracking adaptive synchronous vibration suppression apparatus |
| JP2005315372A (en) * | 2004-04-30 | 2005-11-10 | Japan Science & Technology Agency | Three-dimensional vibration restraining magnetic damper |
| CN102268801A (en) * | 2010-06-03 | 2011-12-07 | 株式会社东芝 | Washing machine |
| CN107491109A (en) * | 2017-08-04 | 2017-12-19 | 南京航空航天大学 | Magnetically levitated flywheel multiple-frequency vibration power suppressing method based on modified multi-resonant controller |
| CN107807533A (en) * | 2017-12-04 | 2018-03-16 | 南京航空航天大学 | Once per revolution vibration torque based on cross decoupling notching method suppresses control method |
| CN108710286A (en) * | 2018-05-22 | 2018-10-26 | 南京航空航天大学 | Once per revolution vibration torque hierarchical control method based on cross decoupling trapper |
| CN109058292A (en) * | 2018-08-09 | 2018-12-21 | 南京航空航天大学 | A kind of novel magnetically levitated direct suppressing method of bearing unbalance vibration power |
| CN109190270A (en) * | 2018-09-12 | 2019-01-11 | 北京化工大学 | A kind of double balancing disk balance Control Scheme methods based on APSO-BP |
| WO2019037063A1 (en) * | 2017-08-25 | 2019-02-28 | 海门市品格工业设计有限公司 | Magnetic bearing detection system based on dsp control |
Family Cites Families (9)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US5285995A (en) * | 1992-05-14 | 1994-02-15 | Aura Systems, Inc. | Optical table active leveling and vibration cancellation system |
| DE10059763A1 (en) * | 2000-11-30 | 2002-06-06 | Otmar Fahrion | Device for measuring a rail segment for a magnetic levitation train |
| US7261487B2 (en) * | 2003-07-31 | 2007-08-28 | Trw Automotive U.S. Llc | Composite ball joint bearing for a ball joint assembly |
| CN100488800C (en) * | 2006-05-22 | 2009-05-20 | 北京前沿科学研究所 | Magnetic suspension anti-knock controller and its control method |
| CN101763038B (en) * | 2009-12-22 | 2012-06-06 | 北京航空航天大学 | Method for controlling structural modal vibration of dual-frame magnetic levitation control moment gyroscope |
| CN104950919B (en) * | 2015-06-17 | 2017-05-17 | 北京航空航天大学 | Method for designing stability parameters of self-adapting filter of self-balancing system of magnetic suspension rotor |
| CN107220456B (en) * | 2017-06-20 | 2020-07-28 | 清华大学 | Control method and device for magnetic suspension shafting falling track identification and re-suspension |
| CN108426692B (en) * | 2018-04-27 | 2023-12-08 | 唐山森普矿山装备有限公司 | Magnetic suspension rotor experiment table and magnetic suspension rotor test analysis method |
| CN109062274B (en) * | 2018-09-03 | 2021-09-10 | 河南工业大学 | Magnetic bearing vibration torque suppression method based on complex variable finite dimension repeated control |
-
2019
- 2019-06-13 CN CN201910511660.9A patent/CN110261083B/en active Active
Patent Citations (11)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| SU435389A1 (en) * | 1972-05-22 | 1974-07-05 | Д. Ф. Сид ков | DEVICE FOR SUSPENSION ROTOR |
| US5400256A (en) * | 1992-01-21 | 1995-03-21 | The Charles Stark Draper Laboratory, Inc. | Frequency tracking adaptive synchronous vibration suppression apparatus |
| CN1088308A (en) * | 1992-05-08 | 1994-06-22 | 蒂德裂纹试验装置公司 | Magnetic detection device for detecting cracks of ferromagnetic workpiece |
| JP2005315372A (en) * | 2004-04-30 | 2005-11-10 | Japan Science & Technology Agency | Three-dimensional vibration restraining magnetic damper |
| CN102268801A (en) * | 2010-06-03 | 2011-12-07 | 株式会社东芝 | Washing machine |
| CN107491109A (en) * | 2017-08-04 | 2017-12-19 | 南京航空航天大学 | Magnetically levitated flywheel multiple-frequency vibration power suppressing method based on modified multi-resonant controller |
| WO2019037063A1 (en) * | 2017-08-25 | 2019-02-28 | 海门市品格工业设计有限公司 | Magnetic bearing detection system based on dsp control |
| CN107807533A (en) * | 2017-12-04 | 2018-03-16 | 南京航空航天大学 | Once per revolution vibration torque based on cross decoupling notching method suppresses control method |
| CN108710286A (en) * | 2018-05-22 | 2018-10-26 | 南京航空航天大学 | Once per revolution vibration torque hierarchical control method based on cross decoupling trapper |
| CN109058292A (en) * | 2018-08-09 | 2018-12-21 | 南京航空航天大学 | A kind of novel magnetically levitated direct suppressing method of bearing unbalance vibration power |
| CN109190270A (en) * | 2018-09-12 | 2019-01-11 | 北京化工大学 | A kind of double balancing disk balance Control Scheme methods based on APSO-BP |
Non-Patent Citations (3)
| Title |
|---|
| "Vibration control of a flexible rotor/magnetic bearing system subject to direct forcing and base motion disturbances";Cole, M O T Keogh,P S Burrows,C R;《Proceedings of the Institution of Mechanical Engineers, Part C:Journal of Mechanical Engineering Science》;19981231;全文 * |
| "基于PC机的磁悬浮轴承实时控制系统的研究";余同正;《中国优秀硕士学位论文全文数据库 工程科技II辑》;20050415(第04（2005）期);全文 * |
| "磁悬浮飞轮不平衡振动控制方法与试验研究";刘彬 等;《机械工程学报》;20100630;第46卷(第12期);全文 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN110261083A (en) | 2019-09-20 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN110261083B (en) | Vision-based method for measuring vibration force suppression effect of magnetic suspension rotor | |
| CN109058292B (en) | A kind of novel magnetically levitated direct suppressing method of bearing unbalance vibration power | |
| CN114326409B (en) | Magnetic suspension rotor direct vibration force suppression method based on double-channel harmonic reconstruction | |
| CN109189114B (en) | A kind of magnetically levitated flywheel oscillatory torque suppressing method based on synchronous rotating angle algorithm | |
| US5084643A (en) | Virtual rotor balancing in magnetic bearings | |
| CN104331565B (en) | The dynamic modeling method and control method of axle class magnetic suspension rigid rotor system | |
| CN109976403B (en) | Method and system for suppressing vibration harmonic waves of magnetic suspension rotor with multiple parallel wave traps | |
| CN110145541A (en) | A kind of magnetic suspension bearing rotor copsided operation control method based on phase stabilization | |
| CN104950919B (en) | Method for designing stability parameters of self-adapting filter of self-balancing system of magnetic suspension rotor | |
| CN110941184A (en) | Sliding mode vibration active control method for electromagnetic bearing flexible rotor different-position system | |
| CN112347717B (en) | Novel method for inhibiting centralized same-frequency disturbance of magnetic bearing | |
| JP2005502004A (en) | Apparatus and method used for automatic compensation of synchronous disturbances | |
| CN111650975B (en) | Magnetic suspension rotor harmonic current suppression method based on multi-order repetitive controller | |
| Peng et al. | Phase-based video measurement for active vibration suppression performance of the magnetically suspended rotor system | |
| CN106289776A (en) | A kind of flexible magnetic suspension bearing rotor stiffness and damping discrimination method | |
| CN109765781A (en) | Same-frequency disturbance suppression method and system | |
| CN115001336A (en) | Vibration control method for rotor of full-speed magnetic suspension high-speed motor | |
| CN113341714B (en) | Method for counteracting same frequency interference of magnetic suspension bearing rotor control system | |
| CN115425817A (en) | High-precision dynamic balance correction device and method for magnetic suspension rotor | |
| CN114371622A (en) | Magnetic suspension rotor harmonic vibration force suppression method based on multi-harmonic inverse Park transformation | |
| CN114322971A (en) | Magnetic suspension rotor same-frequency vibration force suppression method based on biquad generalized integrator | |
| Yu et al. | Unbalanced variation after assembly and double-speed influence coefficient method in the threshing drum | |
| CN113565874A (en) | Magnetic suspension sensor interference suppression method based on variable step length minimum mean square error | |
| CN115016266B (en) | Fractional-order repetitive control-based vibration force suppression method for magnetic suspension rotor system | |
| CN113485472B (en) | Magnetic suspension rotor same-frequency vibration torque suppression method based on double-channel wave trap |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| PB01 | Publication | ||
| PB01 | Publication | ||
| SE01 | Entry into force of request for substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |